## 2632 Analysis of Suspension Bridges

Because a suspension bridge is very flexible and the bridge deck is suspended from the main cables by thin hangers, a different approach from other types of bridge structures should be taken in its analysis.

### 26.3.2.1 Behavior under Vertical Loads

The overall behavior of a suspension bridge is given by the deflection theory where the vertical deflection of cables due to live load is considered in the equilibrium of the structure. The premised assumptions in this case are (1) the cable is completely flexible, (2) the stiffening girder is horizontal and straight, (3) the original form of the main cable is a parabola, (4) all dead loads are sustained by the main cable, and (5) the hangers are inextensible and closely spaced. Thus, the bending moment M(x) of the stiffening girder under live load is given by

where M0(x) is the bending moment due to the live load in a beam without cables, having the same span length, y (x) is the ordinate of the cable, measured from the straight line connecting cable supports, v(x) is the vertical deflection due to live load, Hw and Hp are the horizontal components of cable tension due to dead load and live load, respectively.

It is understood from the above equation that the stiffening girder of a suspension bridge subject to vertical live load can be replaced by the beam shown in Figure 26.8, and the bending moment in the stiffening girder decreases with increase of cable tension and deflection. The longer the span length is, the more conspicuous this effect becomes. In other words, the cable tension very much contributes to the stiffness of a suspension bridge, and since almost all dead loads are sustained by the main cable, the stiffening girder of a suspension bridge is not necessary to be so stiff even if the span is long.

### 26.3.2.2 Behavior under Horizontal Load

Lateral forces caused by wind or earthquake in horizontal direction are to be transmitted from the stiffening girder to the main cables through flexible hangers because the deformation of the girder is larger than that of the main cables due to the difference of the horizontal loads and their stiffness. This effect is more pronounced as seen in Figure 26.9 in the center region of the span owing to large inclination of hangers. Consequently, the lateral bending moment induced in the girder is not so large in the region of the mid-span.

### 26.3.2.3 Design Analysis

Equation 26.2 indicates the nonlinearity between live load and the bridge responses. In long-span suspension bridges, however, Hw + Hp can be assumed nearly constant because Hw is much larger than Hp, and therefore the analysis becomes quasilinear and the influence line analysis can be used on the conservative side (the linearized deflection theory) [9]. This simplified treatment is useful in a very early stage of preliminary design.

More accurate analysis shall be performed at the subsequent design stages including detailed design. With the progress of computer application nowadays, the finite displacement analysis for the entire

suspension bridge structure is available taking into account the discreteness and elongation of hangers, deformation of towers, and so on.

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